4. Definition of Infinite Limit: Let X CR, f: X R and a e X'. If for every M > 0 there exists o > 0 such that |f(r)| > M whenever r EX and 0 < |r - al < 6 then we say that the limit as r approaches a of f(x) is oo which is denoted as lim f(r) = o. Suppose a € R, e > 0, and f, g : N*(a, e) → R. If lim f (x) = L > 0 and lim g(x) = 0, prove lim(fg)(x) = 00 %3D エ→a 全→a エ→a
4. Definition of Infinite Limit: Let X CR, f: X R and a e X'. If for every M > 0 there exists o > 0 such that |f(r)| > M whenever r EX and 0 < |r - al < 6 then we say that the limit as r approaches a of f(x) is oo which is denoted as lim f(r) = o. Suppose a € R, e > 0, and f, g : N*(a, e) → R. If lim f (x) = L > 0 and lim g(x) = 0, prove lim(fg)(x) = 00 %3D エ→a 全→a エ→a
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 56E
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![4. Definition of Infinite Limit: Let XCR, f: X R and a e X'. If for every M > 0
there exists o > 0 such that |f(r)| > M whenever r € X and 0 < |r - al < 6 then we
say that the limit as r approaches a of f(x) is o which is denoted as lim f(x) = 00.
Suppose a € R, e > 0, and f, g : N*(a, e) → R. If lim f (x) = L > 0 and lim g(x) = 00,
エ→a
prove lim(fg)(x) = 00
エ→a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5a7bb65-b92b-4b2a-a8a3-c52d52b3b98d%2F05002be8-de29-4785-877e-bc23cbad326f%2Fjv8503_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Definition of Infinite Limit: Let XCR, f: X R and a e X'. If for every M > 0
there exists o > 0 such that |f(r)| > M whenever r € X and 0 < |r - al < 6 then we
say that the limit as r approaches a of f(x) is o which is denoted as lim f(x) = 00.
Suppose a € R, e > 0, and f, g : N*(a, e) → R. If lim f (x) = L > 0 and lim g(x) = 00,
エ→a
prove lim(fg)(x) = 00
エ→a
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